Critical evaluation of wind speed frequency distribution functions

Abstract

Over the past few years a number of new mathematical functions have been proposed for wind speed probability density distributions. The most commonly used function that has been cited in literature has been the two-parameter Weibull function. However, in recent years studies have shown that the two-parameter Weibull function might be inadequate in modeling the wind speed probability density distributions or independent of whether the distribution is of unimodal or bimodal nature. For the unimodal distributions, the inadequacy may be due to the intricate behavior of the distribution, which prevents it to be satisfyingly modeled by a two-parameter model. For the bimodal behavior, the two-parameter Weibull function, which produces only a unimodal distribution, is simply inadequate to model it appropriately. Therefore, in recent years, alternative functions have been suggested for both unimodal and bimodal distributions, seeking more involved functions to better model these distributions. This article involves the modeling of observed wind speed probability density distributions using the main body of models found in the literature, namely, Rayleigh, Lognormal, two-parameter Weibull, three-parameter Weibull, and bimodal Weibull probability distribution functions. One of the important steps in the evaluation of different functions is the interpretation of the statistical parameters, namely, slope, R2, mean bias error, and root mean squared error, as are presently used in this article. A novel statistical tool is developed in the present article using these four statistical parameters. The novel tool can be used to evaluate the relative performance of models when more than one model is involved or to determine the overall accuracy of a particular model for a specific site. The calculations are made based on the long term wind speed data collected at 4-s interval at the experimental site at Edinburgh Napier University.

A tractable approximation of non-convex chance constrained optimization with non-Gaussian uncertainties

“…Nevertheless, this is not always the case in many practical applications. For instance, the wind speed in wind power generation (Celik, Makkawi, and Muneer 2010) and the clearness index in solar energy (Ibanez, Rosell, and Beckman 2003) are found to be Beta and Gamma distributed, respectively. Therefore, there is a strong practical need for the consideration of nonlinear non-convex chance constrained optimization problems in the presence of non-Gaussian distributed random variables.…”

Wind Power Integration: An Experimental Investigation for Powering Local Communities

“…To assess the wind potential of a particular site, it should be considered that wind energy is a time-varying entity which not only changes the magnitude but also the direction [15][16]. Moreover, above characteristics are significant for adequate evaluation of wind potential available in particular site.…”

A method for including daily patterns to synthetic wind speed data for energy systems planning: Validation in the Azores Islands

“…Different approaches have been used to generate synthetic wind data with hourly timesteps. Kaminsky et al 7 present and compare several such methods including independent and identically distributed values [8][9][10][11][12] one-or two-step Markov chain models, [13][14][15][16] Box-Jenkins or auto-regressive (moving average) (AR(MA)) models, 17 which have been used for synthetic wind speed data, 18 and Markov chain models. 7 They pointed out that most methods lack lower frequency information, i.e., diurnal effects are typically neglected even though autocorrelation for several hours may be included.…”